Journal of applied mathematics & informatics
- Volume 17 Issue 1_2_3
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- Pages.719-736
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- 2005
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- 2734-1194(pISSN)
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- 2234-8417(eISSN)
SURVEY OF GIBBS PHENOMENON FROM FOURIER SERIES TO HYBRID SAMPLING SERIES
- SHIM HONG TAE (Department of Mathematics, Sunmoon University) ;
- PARK CHIN HONG (Department of Mathematics, Sunmoon University)
- Published : 2005.01.01
Abstract
An understanding of Fourier series and their generalization is important for physics and engineering students, as much for mathematical and physical insight as for applications. Students are usually confused by the so-called Gibbs' phenomenon, an overshoot between a discontinuous function and its approximation by a Fourier series as the number of terms in the series becomes indefinitely large. In this paper we give short story of Gibbs phenomenon in chronological order.
Keywords
- Dirichlet kernel;
- Fourier series;
- Gibbs phenomenon;
- Hybrid sampling series;
- sampling series;
- Spline function;
- wavelet series